Serial write time

How many bytes does the UART hold? I just looked back at the PJRC note and the 2 bytes are what the USB chip holds, but the UART must hold at least 1 like SPI doesn't it? So if you fill it, won't the hardware deal with the bits without using any IRQ? Does it flag job complete or will that require an IRQ? The idea being to let other tasks run while the UART is busy by only sending 1 byte at a time so Serial.write() returns more quickly.